A mathematical model is developed to further examine the dynamic interaction of uninfected T cells with Human Immunodeficiency Virus (HIV) mutations. We study how the dynamics are affected by immune response to infected cells under intermittent antiretroviral therapy. Our goal is to analyze the SMART (Strategies for Management of anti-retroviral Therapy) study outcomes and based on that try to identify possible causes of its failure. We mathematically describe the HIV infection and perform numerical simulation to approach the course of the disease. Preliminary results suggest that the scheduling of follow-up visits and working range of CD4+ T cells count used during the SMART study could explain the observed adverse outcomes in that trial.